Work Done by a Varying ForceHow do we "handle" a force that is not constant? That is, how much work is done by a

varyingforce? We know how to find the work done by aconstantforce,W = F s cos How much work is done by a varying force such as this one?

Since we

doknow how to handle aconstant force, we can break this one up into "average values" over small distance x, like this,Each of these little rectangles has an "area" of (F

_{x})(x); this is an amount of work W. That isW = F _{x}xfor each of these little rectangles. The

totalamount of work done is the sum of these rectangles,W _{Tot}= W = WW = F

_{x}xIn the limit, as we make x smaller and smaller, this

sumbecomes anintegral,

Scalar ProductKinetic EnergyReturn to ToC, Ch7, Work and Energy(c) Doug Davis, 2001; all rights reserved